# i want prove when $f$ and $f_{n}$ are non-negative then $\int f\quad d\mu=\sup_{n} \int f_{n}\quad d\mu=\lim_{n\to \infty}\int f_{n}\quad d\mu$

let $f$ and $f_{n}$ are non-negative extended real-valued measurable functions and $f_{n}(\omega)\nearrow f(\omega)$, $\forall \omega \in \Omega$ ,then $$\int f\quad d\mu=\sup_{n} \int f_{n}\quad d\mu=\lim_{n\to \infty}\int f_{n}\quad d\mu$$ thanks for help.